When a recipe calls for shredded Parmesan cheese, use the cheese found in bags in the grocery store dairy section. Shredded Parmesan is often used in salads or soups where the shreds make a pretty garnish. If grated Parmesan is called for, use the finely grated cheese sold in containers with shaker/pourer tops. This type works well in lasagna and casseroles. (You can substitute either shredded or grated Parmesan in equal proportions in your favorite recipes.)
If you decide to buy a chunk of Parmesan cheese and grate your own, be sure to use the finest section on your grating tool. You can also use a blender or food processor. Simply cut the cheese into 1-inch cubes and process 1 cup of cubes at a time on high until finely grated.